We present a novel approach to data storage based on Holographic principles that encodes information in geometric structures rather than discrete units. Building on recent advances in geometric error correction and Holographic duality, we develop a mathematical framework for storing and retrieving information using topological invariants that provide natural error protection. We prove that this approach achieves information preservation without active error correction, leading to inherently robust memory systems. Our framework provides explicit constructions for Encoding classical and quantum data in geometric structures while maintaining error protection through topological invariance. We demonstrate theoretical bounds showing superior error resistance compared to traditional storage methods, along with practical implementation strategies using current technology.

In this paper, we investigate special points in which poles of the Green’s function of the D3/D7 branes are skipping. The system that we consider is SU (N c) N=4 SYM theory coupled to N_f flavors N=2 hypermultplets. We fluctuate the scalar field and find that there is no such special values of frequency and momentum to skip the poles. This behavior is different than scalar field in the AdS black brane background.

In this paper, using complexity equals action proposal, we investigate Holographic complexity for hyperscaling violating theories on different subregions of space-time enclosed by the null boundaries. By recalling the computation of on-shell action for certain subregions of the intersection between the Wheeler DeWitt patch, as well as, the future interior of a two-sided black brane, we are interested in compute uncomplexity in the hyperscaling violating theories [1]. We show that the dynamical exponent plays a crucial role in computing the rate of complexification. However, at the late time, the rate of the complexity growth is independent of the hyperscaling parameters. Moreover, we compute Holographic uncomplexity in hyperscaling violating backgrounds and show when a black hole is formed, uncomplexity is the total space-time volume which is accessible to an observer who decides to pass over the horizon. Therefore, uncomplexity could be considered as a resource which indicates the computational power of a system. In fact, it can extract and analyze the useful information from the system.

In this work we have investigated the inflation mechanism driven by the Barrow Holographic dark energy (BHDE) in the early universe. BHDE is based on the Barrow relation for horizon entropy, which in turn is inspired from the shape of the COVID-19 virus. It was shown by Barrow that the quantum gravitational effects may instigate complex fractal features in the structure of a black hole. Since the length scale during the inflation is expected to be small, the energy density obtained from the application of the Holographic principle in the early universe will be large enough to support the inflationary scenario. Using the Granda-Oliveros IR cut-off we have studied the inflationary scenario with the universe filled with BHDE. Various analytic solutions for the model were found out including the slow-roll parameters, scalar spectral index and tensor-to-scalar ratio. Since inflation is generally attributed to the presence of scalar fields, we have explored a correspondence between BHDE and scalar field models. Both canonical scalar field and the Tachyonic scalar field have been considered for this purpose. The evolution of the potential generated from the fields are plotted and found to be consistent with the observations. From the work we see that BHDE can be a model of dark energy that can successfully drive the early time inflation.

By applying the Holographic method, we study a non-perturbative renormalization group (RG) flow triggered by a gluon condensate. After introducing a bulk scalar field in an AdS space related to the gluon condensate, we investigate the trace anomaly proportional to the gluon condensate. The Holographic calculation reproduces the one-loop trace anomaly known in the lattice QCD. We also show that higher loop corrections give rise to additional contributions and modify the one-loop trace anomaly.

One of the major developments in classical black hole thermodynamics is the inclusion of vacuum energy in the form of thermodynamic pressure. Known as Black Hole Chemistry, this subdiscipline has led to the realization that anti de Sitter black holes exhibit a broad variety of phase transitions that are essentially the same as those observed in chemical systems. Since the pressure is given in terms of a negative cosmological constant (which parametrizes the vacuum energy), the Holographic interpretation of Black Hole Chemistry has remained unclear. In the last few years there has been considerable progress in developing an exact dictionary between the bulk laws of Black Hole Chemistry and the laws of the dual Conformal Field Theory (CFT). Holographic Black Hole Chemistry is now becoming an established subfield, with a full thermodynamic bulk/boundary correspondence, and an emergent understanding of CFT phase behaviour and its correspondence in the bulk. Here I review these developments, highlighting key advances and briefly discussing future prospects for further research.

In this paper, we study some non-local measurements of quantum correlations in extended gravities with higher-order curvature terms, including conformal gravity. Precisely, we consider higher-curvature correction on Holographic mutual information in conformal gravity. There is in fact one deformation in the states because of the higher-curvature corrections. Here by making use of the Holographic methods, we study the deformation in the Holographic mutual information due to the higher-curvature terms. We also address the change in the quantum phase transition due to these deformations.